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If the nucleation rate is given by 
(number of
nuclei
expected in unit time and unit d-dimensional ``volume'') the expected
number of nuclei in the time cone is the integral of 
over
the time cone in space and time.
When 
and 
for 
and 
for
negative time, equation (2.6 can be integrated over space.
For 3-dimensions, this gives
This form is useful for heating and cooling experiments.
Equation (2.7) simplifies
even more when is constant for positive time.
Then 
becomes multiplied by the ``nucleation'' volume
, the volume in space-time of the cone where (and when)
there is nucleation, or equivalently the
volume of the intersection of the cone 
with the constant
nucleation rate domain of 
. Thus when is constant
for positive time
For the classical JMAK theory this intersection of the cone with the
nucleation space
is a right truncated cone, whose volume
is the height 
multiplied by the base 
at 
divided by
The bases and the 
are respectively in 1, 2 and 3
spatial dimensions: 
and 
; 
and 
; and 
and
.